What do the following two equations represent? $2x+3y = -2$ $10x+15y = -4$
Explanation: Putting the first equation in $y = mx + b$ form gives: $2x+3y = -2$ $3y = -2x-2$ $y = -\dfrac{2}{3}x - \dfrac{2}{3}$ Putting the second equation in $y = mx + b$ form gives: $10x+15y = -4$ $15y = -10x-4$ $y = -\dfrac{2}{3}x - \dfrac{4}{15}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.